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Consider a long, thin wire of charge and length .To calculate the average linear charge density, ¯, of this one dimensional object, we can simply divide the total charge, , by the total length, : ¯ = If we describe the wire as having a varying charge (one that varies as a function of position along the length of the wire, ), we can write: = Each infinitesimal unit of charge, , is equal to ...
Heuristically, this can be regarded as nature "attempting" to forecast what the present field would be by linear extrapolation to the present time. [5] The last term, proportional to the second derivative of the unit direction vector e r ′ {\displaystyle e_{r'}} , is sensitive to charge motion perpendicular to the line of sight.
Linear charge density (λ) is the quantity of charge per unit length, measured in coulombs per meter (C⋅m −1), at any point on a line charge distribution. Charge density can be either positive or negative, since electric charge can be either positive or negative. Like mass density, charge density can vary with
Lambda indicates an eigenvalue in the mathematics of linear algebra. In the physics of particles, lambda indicates the thermal de Broglie wavelength; In the physics of electric fields, lambda sometimes indicates the linear charge density of a uniform line of electric charge (measured in coulombs per meter).
Where no such symmetry exists, Gauss's law can be used in its differential form, which states that the divergence of the electric field is proportional to the local density of charge. The law was first [1] formulated by Joseph-Louis Lagrange in 1773, [2] followed by Carl Friedrich Gauss in 1835, [3] both
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Since d 2 = 0, the 3-form J satisfies the conservation of current (continuity equation): = = The current 3-form can be integrated over a 3-dimensional space-time region. The physical interpretation of this integral is the charge in that region if it is spacelike, or the amount of charge that flows through a surface in a certain amount of time ...
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